<!DOCTYPE html>

<html>
  <head>
    <meta charset="utf-8">
    
    <title>numpy.pad &mdash; NumPy v1.18 Manual</title>
    
    <link rel="stylesheet" type="text/css" href="../../_static/css/spc-bootstrap.css">
    <link rel="stylesheet" type="text/css" href="../../_static/css/spc-extend.css">
    <link rel="stylesheet" href="../../_static/scipy.css" type="text/css" >
    <link rel="stylesheet" href="../../_static/pygments.css" type="text/css" >
    <link rel="stylesheet" href="../../_static/graphviz.css" type="text/css" >
    
    <script type="text/javascript">
      var DOCUMENTATION_OPTIONS = {
        URL_ROOT:    '../../',
        VERSION:     '1.18.1',
        COLLAPSE_INDEX: false,
        FILE_SUFFIX: '.html',
        HAS_SOURCE:  false
      };
    </script>
    <script type="text/javascript" src="../../_static/jquery.js"></script>
    <script type="text/javascript" src="../../_static/underscore.js"></script>
    <script type="text/javascript" src="../../_static/doctools.js"></script>
    <script type="text/javascript" src="../../_static/language_data.js"></script>
    <script type="text/javascript" src="../../_static/js/copybutton.js"></script>
    <link rel="author" title="About these documents" href="../../about.html" >
    <link rel="index" title="Index" href="../../genindex.html" >
    <link rel="search" title="Search" href="../../search.html" >
    <link rel="top" title="NumPy v1.18 Manual" href="../../index.html" >
    <link rel="up" title="Padding Arrays" href="../routines.padding.html" >
    <link rel="next" title="Polynomials" href="../routines.polynomials.html" >
    <link rel="prev" title="Padding Arrays" href="../routines.padding.html" > 
  </head>
  <body>
<div class="container">
  <div class="top-scipy-org-logo-header" style="background-color: #a2bae8;">
    <a href="../../index.html">
      <img border=0 alt="NumPy" src="../../_static/numpy_logo.png"></a>
    </div>
  </div>
</div>


    <div class="container">
      <div class="main">
        
	<div class="row-fluid">
	  <div class="span12">
	    <div class="spc-navbar">
              
    <ul class="nav nav-pills pull-left">
        <li class="active"><a href="https://numpy.org/">NumPy.org</a></li>
        <li class="active"><a href="https://numpy.org/doc">Docs</a></li>
        
        <li class="active"><a href="../../index.html">NumPy v1.18 Manual</a></li>
        

          <li class="active"><a href="../index.html" >NumPy Reference</a></li>
          <li class="active"><a href="../routines.html" >Routines</a></li>
          <li class="active"><a href="../routines.padding.html" accesskey="U">Padding Arrays</a></li> 
    </ul>
              
              
    <ul class="nav nav-pills pull-right">
      <li class="active">
        <a href="../../genindex.html" title="General Index"
           accesskey="I">index</a>
      </li>
      <li class="active">
        <a href="../routines.polynomials.html" title="Polynomials"
           accesskey="N">next</a>
      </li>
      <li class="active">
        <a href="../routines.padding.html" title="Padding Arrays"
           accesskey="P">previous</a>
      </li>
    </ul>
              
	    </div>
	  </div>
	</div>
        

	<div class="row-fluid">
      <div class="spc-rightsidebar span3">
        <div class="sphinxsidebarwrapper">
  <h4>Previous topic</h4>
  <p class="topless"><a href="../routines.padding.html"
                        title="previous chapter">Padding Arrays</a></p>
  <h4>Next topic</h4>
  <p class="topless"><a href="../routines.polynomials.html"
                        title="next chapter">Polynomials</a></p>
<div id="searchbox" style="display: none" role="search">
  <h4>Quick search</h4>
    <div>
    <form class="search" action="../../search.html" method="get">
      <input type="text" style="width: inherit;" name="q" />
      <input type="submit" value="search" />
      <input type="hidden" name="check_keywords" value="yes" />
      <input type="hidden" name="area" value="default" />
    </form>
    </div>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
        </div>
      </div>
          <div class="span9">
            
        <div class="bodywrapper">
          <div class="body" id="spc-section-body">
            
  <div class="section" id="numpy-pad">
<h1>numpy.pad<a class="headerlink" href="#numpy-pad" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.pad">
<code class="sig-prename descclassname">numpy.</code><code class="sig-name descname">pad</code><span class="sig-paren">(</span><em class="sig-param">array</em>, <em class="sig-param">pad_width</em>, <em class="sig-param">mode='constant'</em>, <em class="sig-param">**kwargs</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/lib/arraypad.py#L534-L881"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.pad" title="Permalink to this definition">¶</a></dt>
<dd><p>Pad an array.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>array</strong><span class="classifier">array_like of rank N</span></dt><dd><p>The array to pad.</p>
</dd>
<dt><strong>pad_width</strong><span class="classifier">{sequence, array_like, int}</span></dt><dd><p>Number of values padded to the edges of each axis.
((before_1, after_1), … (before_N, after_N)) unique pad widths
for each axis.
((before, after),) yields same before and after pad for each axis.
(pad,) or int is a shortcut for before = after = pad width for all
axes.</p>
</dd>
<dt><strong>mode</strong><span class="classifier">str or function, optional</span></dt><dd><p>One of the following string values or a user supplied function.</p>
<dl>
<dt>‘constant’ (default)</dt><dd><p>Pads with a constant value.</p>
</dd>
<dt>‘edge’</dt><dd><p>Pads with the edge values of array.</p>
</dd>
<dt>‘linear_ramp’</dt><dd><p>Pads with the linear ramp between end_value and the
array edge value.</p>
</dd>
<dt>‘maximum’</dt><dd><p>Pads with the maximum value of all or part of the
vector along each axis.</p>
</dd>
<dt>‘mean’</dt><dd><p>Pads with the mean value of all or part of the
vector along each axis.</p>
</dd>
<dt>‘median’</dt><dd><p>Pads with the median value of all or part of the
vector along each axis.</p>
</dd>
<dt>‘minimum’</dt><dd><p>Pads with the minimum value of all or part of the
vector along each axis.</p>
</dd>
<dt>‘reflect’</dt><dd><p>Pads with the reflection of the vector mirrored on
the first and last values of the vector along each
axis.</p>
</dd>
<dt>‘symmetric’</dt><dd><p>Pads with the reflection of the vector mirrored
along the edge of the array.</p>
</dd>
<dt>‘wrap’</dt><dd><p>Pads with the wrap of the vector along the axis.
The first values are used to pad the end and the
end values are used to pad the beginning.</p>
</dd>
<dt>‘empty’</dt><dd><p>Pads with undefined values.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.17.</span></p>
</div>
</dd>
<dt>&lt;function&gt;</dt><dd><p>Padding function, see Notes.</p>
</dd>
</dl>
</dd>
<dt><strong>stat_length</strong><span class="classifier">sequence or int, optional</span></dt><dd><p>Used in ‘maximum’, ‘mean’, ‘median’, and ‘minimum’.  Number of
values at edge of each axis used to calculate the statistic value.</p>
<p>((before_1, after_1), … (before_N, after_N)) unique statistic
lengths for each axis.</p>
<p>((before, after),) yields same before and after statistic lengths
for each axis.</p>
<p>(stat_length,) or int is a shortcut for before = after = statistic
length for all axes.</p>
<p>Default is <code class="docutils literal notranslate"><span class="pre">None</span></code>, to use the entire axis.</p>
</dd>
<dt><strong>constant_values</strong><span class="classifier">sequence or scalar, optional</span></dt><dd><p>Used in ‘constant’.  The values to set the padded values for each
axis.</p>
<p><code class="docutils literal notranslate"><span class="pre">((before_1,</span> <span class="pre">after_1),</span> <span class="pre">...</span> <span class="pre">(before_N,</span> <span class="pre">after_N))</span></code> unique pad constants
for each axis.</p>
<p><code class="docutils literal notranslate"><span class="pre">((before,</span> <span class="pre">after),)</span></code> yields same before and after constants for each
axis.</p>
<p><code class="docutils literal notranslate"><span class="pre">(constant,)</span></code> or <code class="docutils literal notranslate"><span class="pre">constant</span></code> is a shortcut for <code class="docutils literal notranslate"><span class="pre">before</span> <span class="pre">=</span> <span class="pre">after</span> <span class="pre">=</span> <span class="pre">constant</span></code> for
all axes.</p>
<p>Default is 0.</p>
</dd>
<dt><strong>end_values</strong><span class="classifier">sequence or scalar, optional</span></dt><dd><p>Used in ‘linear_ramp’.  The values used for the ending value of the
linear_ramp and that will form the edge of the padded array.</p>
<p><code class="docutils literal notranslate"><span class="pre">((before_1,</span> <span class="pre">after_1),</span> <span class="pre">...</span> <span class="pre">(before_N,</span> <span class="pre">after_N))</span></code> unique end values
for each axis.</p>
<p><code class="docutils literal notranslate"><span class="pre">((before,</span> <span class="pre">after),)</span></code> yields same before and after end values for each
axis.</p>
<p><code class="docutils literal notranslate"><span class="pre">(constant,)</span></code> or <code class="docutils literal notranslate"><span class="pre">constant</span></code> is a shortcut for <code class="docutils literal notranslate"><span class="pre">before</span> <span class="pre">=</span> <span class="pre">after</span> <span class="pre">=</span> <span class="pre">constant</span></code> for
all axes.</p>
<p>Default is 0.</p>
</dd>
<dt><strong>reflect_type</strong><span class="classifier">{‘even’, ‘odd’}, optional</span></dt><dd><p>Used in ‘reflect’, and ‘symmetric’.  The ‘even’ style is the
default with an unaltered reflection around the edge value.  For
the ‘odd’ style, the extended part of the array is created by
subtracting the reflected values from two times the edge value.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>pad</strong><span class="classifier">ndarray</span></dt><dd><p>Padded array of rank equal to <a class="reference internal" href="numpy.array.html#numpy.array" title="numpy.array"><code class="xref py py-obj docutils literal notranslate"><span class="pre">array</span></code></a> with shape increased
according to <em class="xref py py-obj">pad_width</em>.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 1.7.0.</span></p>
</div>
<p>For an array with rank greater than 1, some of the padding of later
axes is calculated from padding of previous axes.  This is easiest to
think about with a rank 2 array where the corners of the padded array
are calculated by using padded values from the first axis.</p>
<p>The padding function, if used, should modify a rank 1 array in-place. It
has the following signature:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">padding_func</span><span class="p">(</span><span class="n">vector</span><span class="p">,</span> <span class="n">iaxis_pad_width</span><span class="p">,</span> <span class="n">iaxis</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">)</span>
</pre></div>
</div>
<p>where</p>
<blockquote>
<div><dl class="simple">
<dt>vector<span class="classifier">ndarray</span></dt><dd><p>A rank 1 array already padded with zeros.  Padded values are
vector[:iaxis_pad_width[0]] and vector[-iaxis_pad_width[1]:].</p>
</dd>
<dt>iaxis_pad_width<span class="classifier">tuple</span></dt><dd><p>A 2-tuple of ints, iaxis_pad_width[0] represents the number of
values padded at the beginning of vector where
iaxis_pad_width[1] represents the number of values padded at
the end of vector.</p>
</dd>
<dt>iaxis<span class="classifier">int</span></dt><dd><p>The axis currently being calculated.</p>
</dd>
<dt>kwargs<span class="classifier">dict</span></dt><dd><p>Any keyword arguments the function requires.</p>
</dd>
</dl>
</div></blockquote>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="s1">&#39;constant&#39;</span><span class="p">,</span> <span class="n">constant_values</span><span class="o">=</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">6</span><span class="p">))</span>
<span class="go">array([4, 4, 1, ..., 6, 6, 6])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="s1">&#39;edge&#39;</span><span class="p">)</span>
<span class="go">array([1, 1, 1, ..., 5, 5, 5])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="s1">&#39;linear_ramp&#39;</span><span class="p">,</span> <span class="n">end_values</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="o">-</span><span class="mi">4</span><span class="p">))</span>
<span class="go">array([ 5,  3,  1,  2,  3,  4,  5,  2, -1, -4])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,),</span> <span class="s1">&#39;maximum&#39;</span><span class="p">)</span>
<span class="go">array([5, 5, 1, 2, 3, 4, 5, 5, 5])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,),</span> <span class="s1">&#39;mean&#39;</span><span class="p">)</span>
<span class="go">array([3, 3, 1, 2, 3, 4, 5, 3, 3])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,),</span> <span class="s1">&#39;median&#39;</span><span class="p">)</span>
<span class="go">array([3, 3, 1, 2, 3, 4, 5, 3, 3])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">]]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)),</span> <span class="s1">&#39;minimum&#39;</span><span class="p">)</span>
<span class="go">array([[1, 1, 1, 2, 1, 1, 1],</span>
<span class="go">       [1, 1, 1, 2, 1, 1, 1],</span>
<span class="go">       [1, 1, 1, 2, 1, 1, 1],</span>
<span class="go">       [1, 1, 1, 2, 1, 1, 1],</span>
<span class="go">       [3, 3, 3, 4, 3, 3, 3],</span>
<span class="go">       [1, 1, 1, 2, 1, 1, 1],</span>
<span class="go">       [1, 1, 1, 2, 1, 1, 1]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="s1">&#39;reflect&#39;</span><span class="p">)</span>
<span class="go">array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="s1">&#39;reflect&#39;</span><span class="p">,</span> <span class="n">reflect_type</span><span class="o">=</span><span class="s1">&#39;odd&#39;</span><span class="p">)</span>
<span class="go">array([-1,  0,  1,  2,  3,  4,  5,  6,  7,  8])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="s1">&#39;symmetric&#39;</span><span class="p">)</span>
<span class="go">array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="s1">&#39;symmetric&#39;</span><span class="p">,</span> <span class="n">reflect_type</span><span class="o">=</span><span class="s1">&#39;odd&#39;</span><span class="p">)</span>
<span class="go">array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="s1">&#39;wrap&#39;</span><span class="p">)</span>
<span class="go">array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">pad_with</span><span class="p">(</span><span class="n">vector</span><span class="p">,</span> <span class="n">pad_width</span><span class="p">,</span> <span class="n">iaxis</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">):</span>
<span class="gp">... </span>    <span class="n">pad_value</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;padder&#39;</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span>
<span class="gp">... </span>    <span class="n">vector</span><span class="p">[:</span><span class="n">pad_width</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span> <span class="o">=</span> <span class="n">pad_value</span>
<span class="gp">... </span>    <span class="n">vector</span><span class="p">[</span><span class="o">-</span><span class="n">pad_width</span><span class="p">[</span><span class="mi">1</span><span class="p">]:]</span> <span class="o">=</span> <span class="n">pad_value</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">pad_with</span><span class="p">)</span>
<span class="go">array([[10, 10, 10, 10, 10, 10, 10],</span>
<span class="go">       [10, 10, 10, 10, 10, 10, 10],</span>
<span class="go">       [10, 10,  0,  1,  2, 10, 10],</span>
<span class="go">       [10, 10,  3,  4,  5, 10, 10],</span>
<span class="go">       [10, 10, 10, 10, 10, 10, 10],</span>
<span class="go">       [10, 10, 10, 10, 10, 10, 10]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">pad_with</span><span class="p">,</span> <span class="n">padder</span><span class="o">=</span><span class="mi">100</span><span class="p">)</span>
<span class="go">array([[100, 100, 100, 100, 100, 100, 100],</span>
<span class="go">       [100, 100, 100, 100, 100, 100, 100],</span>
<span class="go">       [100, 100,   0,   1,   2, 100, 100],</span>
<span class="go">       [100, 100,   3,   4,   5, 100, 100],</span>
<span class="go">       [100, 100, 100, 100, 100, 100, 100],</span>
<span class="go">       [100, 100, 100, 100, 100, 100, 100]])</span>
</pre></div>
</div>
</dd></dl>

</div>


          </div>
        </div>
          </div>
        </div>
      </div>
    </div>

    <div class="container container-navbar-bottom">
      <div class="spc-navbar">
        
      </div>
    </div>
    <div class="container">
    <div class="footer">
    <div class="row-fluid">
    <ul class="inline pull-left">
      <li>
        &copy; Copyright 2008-2019, The SciPy community.
      </li>
      <li>
      Last updated on Feb 20, 2020.
      </li>
      <li>
      Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 2.4.2.
      </li>
    </ul>
    </div>
    </div>
    </div>
  </body>
</html>